Problem: What do the following two equations represent? $-3x+3y = 3$ $-6x-6y = -4$
Solution: Putting the first equation in $y = mx + b$ form gives: $-3x+3y = 3$ $3y = 3x+3$ $y = 1x + 1$ Putting the second equation in $y = mx + b$ form gives: $-6x-6y = -4$ $-6y = 6x-4$ $y = -1x + \dfrac{2}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.